(1):
Find all irreducible polynomials of the form , where a,b belong to the field with 3 elements.
Show explicitly that is a field by computing its multiplicative monoid.
Identify [ ]* as an abstract group.
any suggestions please?
(1):
Find all irreducible polynomials of the form , where a,b belong to the field with 3 elements.
Show explicitly that is a field by computing its multiplicative monoid.
Identify [ ]* as an abstract group.
any suggestions please?
Just list all of them there are only or them. Now, just check which ones have zeros (there are only three zeros to check). And this tells you which are irreducible and which are not.
Any element in has form . Now show that these elements form a field.Show explicitly that is a field by computing its multiplicative monoid.
Identify [ ]* as an abstract group.